Finite Group Databasebeta

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Dic3×#3968 #14295488

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic3×#3968

Splittings

HallC3×C5 ⋊ C4×#101
SylowC5 ⋊ Dic3×#101
SylowC3 ⋊ C4×#3968

Subgroups

subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC22×C3×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5C4×#101
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21186);